152 BELL SYSTEM TECHNICAL JOURNAL 



and therefore changes from path to path.'^^ ^t the same time there are 

 certain frequencies which give results which are poorer than those 

 obtained with higher or lower frequencies. It is obviously desirable 

 to avoid these in practice. In general, it seems important that in 

 making a choice of frequency, the particular path should be con- 

 sidered by itself in order to insure that maximum transmission 

 efficiency, or at least the best compromise with apparatus difficulties, 

 will be obtained. 



A cknowledgment 



The experiments described in this paper have been possible only 

 through the assistance of many members of the Bell Telephone 

 Laboratories and we wish to make acknowledgment of this cooperation. 

 We also wish to express our appreciation of the support and encourage- 

 ment given in the course of this work by Dr. W. Wilson. 



Appendix I — Reflection Calculations 



The ratio of the resultant of the direct and reflected weaves to the 

 direct wave is 



Vl -\- K^ - 2K cos 7 = V(l - Ky + AK sin^ (7/2), 



where K is the ratio of the amplitude of the reflected wave to that of 

 the direct wave and 7 ± x is their phase difference. 



7 = ^ — A, 



where A is 27r times the path difference in wave-lengths and 



(f = \p zL T 



is the phase advance at reflection. The convention here used for 

 phase change at reflection is the change in phase of the vertical com- 

 ponent in the case of vertical polarization, and the change in phase of 

 the horizontal component in the case of horizontal polarization. In 

 the case of vertical polarization this is different from the convention 



^ Beverage, Peterson and Hansell ("Application of Frequencies above 30,000 kc. 

 to Communication Problems," Proc. I. R. E., 19, 1313-1333, August 1931) found that 

 a maximum range was obtained with a frequency of 35 mc. in some tests made over 

 sea water. This maximum, if not due to peculiarities of the apparatus, it would 

 seem, must be a function of the heights of transmitting and receiving antennas 

 above sea level and above local ground. 



